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Solving a class of multivariate integration problems via Laplace techniques

Jean B. Lasserre, Eduardo S. Zeron (2001)

Applicationes Mathematicae

We consider the problem of calculating a closed form expression for the integral of a real-valued function f:ℝⁿ → ℝ on a set S. We specialize to the particular cases when S is a convex polyhedron or an ellipsoid, and the function f is either a generalized polynomial, an exponential of a linear form (including trigonometric polynomials) or an exponential of a quadratic form. Laplace transform techniques allow us to obtain either a closed form expression, or a series representation that can be handled...

Some results on convergence acceleration for the E-algorithm

A. Fdil (1997)

Applicationes Mathematicae

Some new results on convergence acceleration for the E-algorithm which is a general extrapolation method are obtained. A technique for avoiding numerical instability is proposed. Some applications are given. Theoretical results are illustrated by numerical experiments

Special Classes of Orthogonal Polynomials and Corresponding Quadratures of Gaussian Type

Milovanovic, Gradimir V., Cvetkovic, Aleksandar S. (2012)

Mathematica Balkanica New Series

MSC 2010: 33C47, 42C05, 41A55, 65D30, 65D32In the first part of this survey paper we present a short account on some important properties of orthogonal polynomials on the real line, including computational methods for constructing coefficients in the fundamental three-term recurrence relation for orthogonal polynomials, and mention some basic facts on Gaussian quadrature rules. In the second part we discuss our Mathematica package Orthogonal Polynomials (see [2]) and show some applications to problems...

Splines in Numerical Integration

Udovičić, Zlatko (2010)

Mathematica Balkanica New Series

AMS Subj. Classification: 65D07, 65D30.We gave a short review of several results which are related to the role of splines (cardinal, centered or interpolating) in numerical integration. Results deal with the problem of approximate computation of the integrals with spline as a weight function, but also with the problem of approximate computation of the integrals without weight function. Besides, we presented an algorithm for calculation of the coefficients of the polynomials which correspond to the...

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